Can my husband get out of out lease without my consent?

I don't see how he could just take himself off of the lease. That's a legal contract between the 2 of you and the landlord. I can't imagine the landlord being willing to remove a name from the lease without discussing it with all parties present either. That doesn't mean there aren't unethical landlords that would do this but I doubt it.

Do you have your original copy of the lease or did hubby take that with him? If so you need to demand that back or get a copy of the original from the landlord. If your husband left you in a financial pickle he needs to pay on the commitment he made of this lease and help you work out breaking the lease or provide financial assistance to you. That's the right and fair thing he should do especially since he knows the predicament he's put you in.

if he signed the lease, he is bound by it